Question

James deposits a fixed monthly amount into an annuity account for his child's college fund. He wishes to accumulate a future value of
$90,000 in 14 years. Assuming an APR of 3.3 % compounded monthly, how much of the $90,000 will James ultimately deposit in the
account, and how much is interest earned? Round your answers to the nearest cent, if necessary.

Answer 1

To solve for the monthly deposit amount, we can use the future value of an annuity formula:

FV = P * (((1 + r)^n - 1) / r)

Where:

FV = Future value (in this case, $90,000)

P = Monthly deposit amount

r = monthly interest rate

n = number of periods

First, we need to convert the yearly interest rate to a monthly rate:

r = 3.3% = 0.033 (in decimal)

We also need to convert the number of years to months:

n = 14 years * 12 months/year = 168 months

Now we can rearrange the formula to solve for the monthly deposit amount:

P = FV / (((1 + r)^n - 1) / r)

P = $90,000 / (((1 + 0.033)^168 - 1) / 0.033)

P ≈ $381.43

So, James will ultimately deposit approximately $381.43 each month into the annuity account.

To calculate the total amount deposited, we can multiply the monthly deposit amount (P) by the number of months (n):

Total amount deposited = Monthly deposit amount * Number of months

Total amount deposited ≈ $381.43/month * 168 months

Total amount deposited ≈ $64,095.24

To find the interest earned, we can subtract the total amount deposited from the future value:

Interest earned = Future value - Total amount deposited

Interest earned ≈ $90,000 - $64,095.24

Interest earned ≈ $25,904.76

Therefore, James will ultimately deposit approximately $64,095.24 into the account, and the interest earned will be approximately $25,904.76.